Problem: Solve for $x$ : $x^2 - 14x + 49 = 0$
Solution: The coefficient on the $x$ term is $-14$ and the constant term is $49$ , so we need to find two numbers that add up to $-14$ and multiply to $49$ The number $-7$ used twice satisfies both conditions: $ {-7} + {-7} = {-14} $ $ {-7} \times {-7} = {49} $ So $(x - {7})^2 = 0$ $x - 7 = 0$ Thus, $x = 7$ is the solution.